What would such an argument be like? Well, arguments that merely fail
to provide any support whatever for their conclusions are two a penny;
a worst conceivable argument for any proposition must surely
be one that actually conclusively refutes the proposition
it's meant to support.

Now, the worst conceivable argument for theism clearly
exists
in the understanding. But it cannot exist only there,
for so bad an argument is of course worse (because more
destructive) if it is actually made; so if it existed only
in the understanding then a worse would be conceivable,
which is a contradiction.

Therefore, there is an argument for theism which is in reality
a conclusive refutation of theism.

But a belief that can be conclusively refuted is false. Therefore
there is no God.

Note: Yes, of course the above is entirely
ridiculous,
and in particular I am of course not suggesting that it actually
offers the slightest reason for rejecting theism.